Starve

To starve is to die from lack of nutrition. Starvation was a permanent spectre of the medieval era, a time that lacked refrigeration or all but the most basic methods of food preservation. One bad harvest could cause widespread starvation and famine.

A siege was an attempt to "starve out" a fortified position, that is, to cut off the flow of supplies and force the defenders to surrender before their supplies ran out.